Showing papers by "Andrew L. Rukhin published in 2009"
TL;DR: The usefulness of weighted mean statistics as a consensus mean estimator in collaborative studies is discussed in this article, where a random effects model designed to combine information from several sources is employed to justify their appeal to metrologists.
Abstract: The usefulness of weighted means statistics as a consensus mean estimator in collaborative studies is discussed. A random effects model designed to combine information from several sources is employed to justify their appeal to metrologists. Some methods of estimating the uncertainties and of constructing confidence intervals are reviewed.
74 citations
12 Jan 2009
TL;DR: The goals of this chapter are to discuss different approaches to uncertainty assessment from a statistical point of view and to relate them to the methods that are currently being used in metrology or being developed within the metrology community.
Abstract: Since its adoption, the ISO Guide has sparked a revolution in uncertainty analysis. Of course, even with all of the positive contributions from the development and adoption of the ISO Guide, there will always be a need to improve the assessment of uncertainty in particular applications and to extend it to cover new areas. Among other work along these lines, the International Committee on Weights and MeasuresÂ’ Joint Committee on Guides in Metrology is currently working on several supplements to the ISO Guide. Other authors have also recently made many important contributions to the theory and practice of uncertainty analysis. The goals of this chapter are to discuss different approaches to uncertainty assessment from a statistical point of view and to relate them to the methods that are currently being used in metrology or are being developed within the metrology community. The particular statistical paradigms under which different methods for uncertainty assessment are described include the frequentist, Bayesian, and fiducial paradigms. Each approach is illustrated using common examples and computer code for carrying out each analysis is illustrated using open-source software.
18 citations
TL;DR: The accepted definitions of confidence level and of critical value are reviewed and the testing requirements for establishing either of these probabilities at a desired confidence level are described.
Abstract: Performance standards for detector systems often include requirements for probability of detection and probability of false alarm at a specified level of statistical confidence. This paper reviews the accepted definitions of confidence level and of critical value. It describes the testing requirements for establishing either of these probabilities at a desired confidence level. These requirements are computable in terms of functions that are readily available in statistical software packages and general spreadsheet applications. The statistical interpretations of the critical values are discussed. A table is included for illustration, and a plot is presented showing the minimum required numbers of pass-fail tests. The results given here are applicable to one-sided testing of any system with performance characteristics conforming to a binomial distribution.
14 citations
TL;DR: In this article, two formulas for the central inverse moments of a quadratic form in normal variables and of the ratio of such forms were established, which relates the quadrastic form determined by a positive definite matrix to that defined by the inverse matrix.
2 citations
TL;DR: In this article, the problem of guaranteeing the necessary sample size is formulated as that of open-ended hypothesis testing, and the formulas for the probabilities of general stopping time distribution are derived for the linear boundary they are in the class of Lagrangian Poisson distributions.
Abstract: This article addresses the sequential sampling issues related to attainment of a given number of subjects in a Poisson arrival process. The problem of guaranteeing the necessary sample size is formulated as that of open-ended hypothesis testing. To implement the procedure a one-sided stopping boundary must be specified. The formulas for the probabilities of general stopping time distribution are derived. For the linear boundary they are in the class of Lagrangian Poisson distributions. A locally optimal test is obtained.
2 citations
TL;DR: The first regional key comparison in vibration conducted under the auspices of the Inter American System of Metrology (SIM) was begun in 1996 and was registered with the International Bureau of Weights and Measures (BIPM) through the Consultative Committee for Acoustics, Ultrasound and Vibration (CCAUV) under the key comparison designation of SIM.AUV.V K1 as discussed by the authors.
Abstract: The first regional key comparison in vibration conducted under the auspices of the Inter American System of Metrology (SIM) was begun in 1996. The comparison was registered with the International Bureau of Weights and Measures (BIPM) through the Consultative Committee for Acoustics, Ultrasound and Vibration (CCAUV) under the key comparison designation of SIM.AUV.V K1. The national measurement institutes (NMIs) of five countries participating in SIM performed and reported calibrations of one back-to-back and two single-ended accelerometers for this comparison during the time period of 1997 to 1999. The participants in the comparison were: Argentina (INTI), Brazil (INMETRO), Canada (NRC), Mexico (CENAM) and the United States (NIST). Reference Values (RVs) were established for the SIM.AUV.V-K1 comparison using maximum likelihood consensus estimation applied to the summary values of charge sensitivity with the nominal numbers of repeat measurements reported by the participating NMIs. Degrees of equivalence between the results reported by the NMIs and the RVs as well as pairwise degrees of equivalence between the results reported by the NMIs were computed using the uncertainties associated with the results reported by the NMIs and those of the RVs as appropriate. Transformation values were found in order to link the results of SIM.AUV.V-K1 with those of the first international key comparison in vibration conducted under the auspices of the CCAUV during 1999 to 2001 (CCAUV.V-K1). The degrees of equivalence between the NMIs participating in SIM.AUV.V-K1 and those participating in CCAUV.V-K1 were established using linkage values computed from the transformation values. Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCAUV, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).
1 citations
TL;DR: In this paper, the authors studied properties of conservative confidence ellipsoids for parameters of a general linear model and showed the relationship of this problem to moments of quadratic forms in Gaussian random variables and to multiple hypergeometric functions.
Abstract: This paper studies properties of conservative confidence ellipsoids for parameters of a general linear model. These regions are obtained on the basis of a linear estimator when only a vague knowledge of (heterogeneous) error variances is available. The required optimization problem is formulated and the solution space is described. The relationship of this problem to moments of quadratic forms in Gaussian random variables and to multiple hypergeometric functions is demonstrated. We explore the situation when the least favorable variances are equal. An example of a telephone switching study is considered.